Nice question. Your understanding of ～ておく is correct. I looked at this source, and found that their translation was "do something in advance." I totally agree with that from my personal experience.
Your example sentence is a great example sentence. You are right to question "what is this being done in advance of?"
You could easily say:
and have the same meaning when translated into English. The Japanese, however, is different in feel, not necessarily in translation.
The difference here is the implication that comes with it. I'm going to take the translation you have, and add in parenthesis the implication. Hopefully that will help clear things up.
Because we don't need that paper, please throw it away (so we won't have to later).
We are throwing the paper away in advance of needing to throw it away later.
I wonder if Te Oku has another meaning. Is that right?
The answer is no, there is not another meaning of ～ておく. In this sentence, it is used correctly, just maybe counter-intuitive at first.